The commissioner of the Metropolitan police, Sir Paul Stephenson, said today that armed officers protecting Prince Charles and his wife Camilla as their car was attacked by student protesters showed "enormous restraint" and condemned the "thugs" who attacked the vehicle.

He defended his force as questions were asked of the police over how the royal couple became embroiled in the protest in the wake of a Commons vote to treble tuition fees for students in England.

The commissioner said it was a "hugely shocking incident and there will be a full criminal investigation" but added "short of locking everything down we have to try and find that balance" of allowing protest and stopping violence. He praised his officers and the royal protection officers for their actions on coping with a "very unpredictable demonstration ... and very difficult night ... They showed enormous restraint in the most difficult of circumstances."

Stephenson was supported by the mayor of London, Boris Johnson, who said that there would inevitably be questions of "why exactly they [Charles and Camilla] were on that route", but defended the police, saying it was regrettable people's first reaction was to attack the police.

He said a balance had to be struck between allowing protest and proportionate policing, saying the country could have "different system", using watercannon and harsher police tactics that would have left "more broken heads this morning".

Earlier Brian Paddick, a former deputy assistant commissioner with the Metropolitan police, told ITV's Daybreak: "I don't think that Prince Charles and Camilla should have ever found themselves in that situation. They should have had motorcycle outriders well in advance of the car who should have seen what was around the corner and diverted them on another route."

Their car – a Rolls Royce – was surrounded by a mob as it drove down Regent Street en route to a Royal Variety performance, with protesters kicking at the doors and shattering a rear window.

Dai Davies, a former head of the Metropolitan police Royalty and Diplomatic section, told BBC Radio 4's Today programme that there should have been better coordination between the policing of the protest and the protection around the prince.

The protesters had spilled into the West End after an initially peaceful demonstration outside parliament had rapidly deteriorated and spread; there were clashes in Parliament Square and windows at the Treasury was smashed as students chanted: "We want our money back."

Witnesses described how around 400 to 500 protesters were on Regent Street when the royal car was attacked. One, Ben Kelsey, said "it was fairly obvious who was in the car. It was very well lit up". The royal couple were taken aback by the attack but later joked about the incident.

A total of 34 protesters were arrested. Dozens of protesters and a number of officers were injured.

David Davis, the former shadow home secretary, told the Daily Telegraph: "Sir Paul has very serious questions to answer about this operation. The police always know where the prince is for obvious security reasons.

"So why were professional anarchists and violent agitators allowed to come anywhere near his car?"

The home secretary, Theresa May, said the "next steps" in relation to the attack were down to the Metropolitan police.

Charles and Camilla were visibly shaken but unharmed after up to 20 demonstrators set upon the vehicle with fists, boots and bottles, chanting "Off with their heads" and "Tory scum".

One witness said Charles kept calm, gently pushing his wife towards the floor to get her out of the line of fire.

"Charles got her on the floor and put his hands on her," said Adnan Nazir, a 23-year-old podiatrist who was following the protesters.

Davies said he was "appalled" at the "atrocious attack".

He told the BBC: "One of the principles of protection is to have alternative routes and I would expect there to be at least three different routes, and I'm surprised.

"Clearly the commissioner is embarrassed and surprised; also, why there isn't better co-ordination between those in charge of protection and those marshalling and dealing with the riots we saw?"

Davies added: "Presumably someone must have told royal protection there was a demonstration of this sort and intelligence should have co-ordinated a better system. I'm sure my successor is looking very carefully at what went wrong and indeed how it must never happen again.

"It was an atrocious attack on their two royal highnesses and I'm appalled, frankly."

Mark Pritchard, the Conservative MP for the Wrekin, also questioned police tactics, telling the BBC: "We've got 'kettling' that is supposed to confine people in an area to stop violence spilling out to other areas, and clearly it has not worked. Therefore, the planning and control and the senior management decisions by the Metropolitan police over this whole incident need to be looked at."